Backlund transformation of fractional Riccati equation and its applications to the space-time FDEs

被引：12

作者：

Arnous, A. H. ^{[1
]}

Mirzazadeh, M. ^{[2
]}

机构：

[1] Higher Inst Engn, Dept Engn Math & Phys, El Shorouk, Egypt

[2] Univ Guilan, Fac Math Sci, Dept Math, Rasht, Iran

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2015年 / 38卷 / 18期

关键词：

nonlinear partial differential equations; space-time FDEs; fractional Riccati equation; PARTIAL-DIFFERENTIAL-EQUATIONS; ORDER;

D O I：

10.1002/mma.3371

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the Backlund transformation of fractional Riccati equation is presented to establish traveling wave solutions for two nonlinear space-time fractional differential equations in the sense of modified Riemann-Liouville derivatives, namely, the space-time fractional generalized reaction duffing equation and the space-time fractional diffusion reaction equation with cubic nonlinearity. The proposed method is effective and convenient for solving nonlinear evolution equations with fractional order. Copyright (C) 2014 John Wiley & Sons, Ltd.

引用

页码：4673 / 4678

页数：6

共 16 条

[1]

[Anonymous], 1999, MATH SCI ENG

[2]

[Anonymous], 2010, NEW TRENDS NANOTECHN

[3] Compact finite difference method for the fractional diffusion equation [J].

Cui, Mingrong .

JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 228 (20) :7792-7804

[4] The Adomian decomposition method for solving partial differential equations of fractal order in finite domains [J].

El-Sayed, A. M. A. ;

Gaber, M. .

PHYSICS LETTERS A, 2006, 359 (03) :175-182

[5] Application of first integral method to fractional partial differential equations [J].

Eslami, M. ;

Vajargah, B. Fathi ;

Mirzazadeh, M. ;

Biswas, A. .

INDIAN JOURNAL OF PHYSICS, 2014, 88 (02) :177-184

[6] Solution of nonlinear fractional differential equations using homotopy analysis method [J].

Ganjiani, Mehdi .

APPLIED MATHEMATICAL MODELLING, 2010, 34 (06) :1634-1641

[7] The improved fractional sub-equation method and its applications to the space-time fractional differential equations in fluid mechanics [J].

Guo, Shimin ;

Mei, Liquan ;

Li, Ying ;

Sun, Youfa .

PHYSICS LETTERS A, 2012, 376 (04) :407-411

[8] The approximate and exact solutions of the space- and time-fractional Burgers equations with initial conditions by variational iteration method [J].

Inc, Mustafa .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 345 (01) :476-484

[9] Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results [J].

Jumarie, G. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2006, 51 (9-10) :1367-1376

[10]

Lakshmikantham V., 2009, Theory of fractional dynamic systems

← 1 2 →